In an interview to London-based newspaper al-Hayat published Monday, Yousef said: "We have presented a number of questions to the Israelis and are awaiting answers."
Yousef also stressed that Hamas was determined to maintain its good relations with Egypt and would not allow its security to be undermined.
According to al-Hayat, Hamas' leaders in Damascus have sent former US President Jimmy Carter a document detailing their comments on his proposal for a truce between the group and Israel.
Meanwhile, Hamas is also looking into Egypt's proposal for a truce in Gaza first, and in the West Bank as a second stage.
While Hamas officials refused to disclose the content of their letter to Carter, it is estimated that the movement would be willing to show some flexibility on the offer.